A New LBGK Scheme For The Convection Diffusion Equations With Variable Coefficients

The convection diffusion equation shows a lot of interest in biomathematics, chemistry and physics, etc. It could describe the transformation of mass and heat, and also describe many physical phenomenons as well as the reaction diffusion equation. Meanwhile, in the last few years, the lattice Boltzmann method (LBM), known as an alternative method for fluid dynamics, attracts a lot of attention which makes great progress of computation and simulation in many fields, such as electro-osmotic flow, magneto-hydrodynamic flow, multi-phase fluids, flow through porous media and so on.However, the application of LBM in the convection diffusion equation (CDE) has not achieved so much great successes. Most of the current LB models for CDE handle with constant velocity. In the practical applications, a constant velocity is a special and approximated case. Though some articles on applications of LBE discussed about some variable velocity, they are usually based on some assumptions. Previous work shows that those CD equations with variable coefficients are popular in the nature.A new scheme to eliminate the constrain on velocity need to be proposed and discussed. In this thesis, a novel scheme for CDE has proposed to overcome the short-comings above. This scheme originates from the LBGK model but with an extra term in the evolution equation. The numerical experiments show that the LBE can be used to solve the convection diffusion problems with variable coefficients.